More companies are cutting ties to a U.S.-owned Chinese food supplier over worries that they may have served expired meat to their customers, as they moved to shore up their reputations in a market known for food-safety problems.

The issue, which on Monday prompted KFC owner Yum Brands Inc. and McDonald's Corp.'s China arm to drop the China-based food supplier, on Tuesday spread to Japan. McDonald's on Tuesday said its outlets there cut ties with Shanghai Husi Food Co., an arm of OSI Group Inc. of Aurora, Ill. Shanghai...